The concepts of optimization and diversification of the portfolio have been fundamental for the development and understanding of the financial markets and the financial decison making. For this reason, it is appropriate to review the portfolio optimization methods in light of the theory of fuzzy decision. Therefore, in the first part of this paper, a review of risk measures used in the selection of portfolios is done highlighting both its advantages and disadvantages. In the second part, the analysis of the portfolio selection methods is done based on the fuzzy mathematical programming and those where the imprecision and uncertainty of future performance are modeled through possibility and credibility distributions.